M
ASSACHUSETTS
I
NSTITUTE OF
T
ECHNOLOGY
15.053 – Optimization Methods in Management Science (Spring 2007)
Problem Set 11, Due December 3
rd
2013
You will need 0 points out of 0 to receive a grade of 0
Prologue:
Nooz, feeling he was promised an equal starring role in the course, and in the end taking
a backseat to Ollie and Tim, decides to leave the course to pursue a few “real world
jobs”. Will this sly fox make it in the real world and cease to exist as a 15.053 character
or return to his role as our number one fox? In this problem set, we follow the adventures
of Nooz while learning about our final topic decision analysis.
Problem 1:
Nooz Shakes the Steak
Nooz’s Chicken Coop and Steak and Shake are two competing restaurants.
Each must
determine simultaneously whether to undertake small, medium, or large advertising
campaigns. Nooz believes that it is equally likely that Steak and Shake will undertake a
small, a medium, or a large advertising campaign.
Given the actions chosen by each
restaurant, Nooz’s profits are as shown below.
Steak and Shake
Chooses
Nooz Chooses
Small
Medium
Large
Small
4,000
3,000
2,000
Medium
5,000
4,000
3,000
Large
6,000
5,000
1,500
Determine Nooz’s choice under the following decision criteria:
Part A:
maximin
Part B:
maximax
Part C:
minimax regret
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expected value (here, assume Steak and Shake’s three choices are equally likely.)
Problem 2:
Foxes and Fools
Having lost the fast food battle; Nooz decides to start a new News station called Fox
Nooz. The Fox Nooz station generates a profit of $5 million on average for a new show
that becomes a hit, and loses $1 million on average for a show that is a failure. Of all
shows that Fox Nooz is considering, they expect that 30% of them will be a hit and 70%
will be a failure.
For the cost of $500,000, the station can make a pilot that will indicate whether or not a
show will be a hit or a failure. If the pilot is a hit, the series will be a hit with 100%
probability. If the pilot is a failure, then with 100% probability it will be a failure.
(In
practice, pilots are not so reliable as indicators, and the numbers are chosen here to make
the problem simpler.)
Fox Nooz is thinking of producing the new reality series entitled, ‘Who Is the Biggest
Fool: Bill Clinton or Turkey Tim?’.
The show puts two Democrats against each other in
a variety of clownlike challenges. Fox Nooz needs to decide whether or not to produce
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 Spring '07
 JamesOrli
 Management, Probability theory, probability density function

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